# Geology Lab- Relative and Absolute Time Scales

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Lab 6A: Relative and absolute dating of geologic events
Part A: Relative Time Scales
Introduction
The study of Earth history involves determining the sequence of geologic events over
immense spans of time. In most cases the correct order of events can be determined
without knowing their actual ages: that is, we simply establish that event B occurred
before event C, but after event A. Such dating, in which the occurrence of events is
determined relative to one another, is known as relative dating. Of course it is always
useful to know the actual ages of rocks and events, if possible. Actual ages are
determined by means of radiometric dating techniques. Although several techniques
exist, all rely on the fact that radioactive “parent” isotopes decay into stable “daughter”
isotopes at a constant rate. With knowledge of the decay rate, ratios of parent and
daughter isotopes then can be used to derive an absolute date, in years, for
the age of a given mineral sample. The purpose of this lab is to introduce the principles
and concepts associated with both relative and absolute dating.
Relative dating
The relative order of geologic events can be established in most cases by applying four
or fewer basic principles:
1) The Principle of Original Horizontality states that sedimentary rocks are deposited
as horizontal or nearly horizontal layers. Any marked deviation from horizontality
indicates that some movement or deformation of the Earth’s crust occurred after
deposition of the inclined layer.
2) The Principle of Superposition states that in an ordinary vertical sequence of
sedimentary rocks, the layer at the bottom of the sequence is oldest, and successively
higher layers are successively younger.
3) The Principle of Cross-cutting relationships states that geologic features such as
faults and igneous intrusions, which cut through rocks, must be younger than the rocks
through which they cut.
4) The Principle of Inclusion states that if rocks or rock fragments are included within
another rock layer, the rock fragments must be older than the layer in which they are
included.
Complete Exercises I – V on the following pages.
Unconformities: Unconformities are especially useful in reconstructing Earth history.
An unconformity is a surface that corresponds with a gap in sedimentation,
either non-deposition or erosion. Rocks above an unconformity are younger than those
below it.
Three main types of unconformities are recognized (Figure 1):
1) angular unconformity, in which beds above and below the surface are not parallel
2) nonconformity, in which sedimentary layers overly crystalline rocks (either igneous
or metamorphic)
3) disconformity, in which beds above and below the surface are parallel, but the
surface itself is irregular, exhibiting evidence of erosional relief. In geologic block
diagrams and cross-sections, unconformities are usually drawn as a wavy line.
Figure 1
There is also a fourth type called a paraconformity where there is no obvious break in
the sedimentary record, but other evidence points to missing time.
I. Unconformities Exercises:
Figure 2: Possible unconformities
A
B
C
For each of the above, determine whether there is an unconformity. Give your reasoning
for each example above. Determine any missing time for the unconformities identified.
A:
B:
C:
II. Principle of Inclusions
Figure 3: Relative age from inclusion
D
E
For each of the above, determine the relative ages
D:
E:
F:
F
III. Principle of cross-cutting relations
Figure 4: Relative age determination using cross-cutting relations
G
H
I
For each of the above, determine the relative ages
G:
H:
I:
IV. Relative Dating Exercises – Telling the Story
For each of the following four block diagrams (A–D), determine the correct order in
which the various rock units and other features occurred. Write a summary for each
section detailing the occurrence of any unconformities and the timing of any intrusions
geologic structures etc.
A.
B.
C.
D.
Summary Paragraphs: Include in your summaries how the 4 principles outlined in
Diagram A:
Diagram B:
Diagram C:
Diagram D:
Part B: ABSOLUTE TIME SCALES
Background: Determination of the actual age, in years, of minerals is accomplished by
occurring isotopes are radioactive and their decay rates are constant. The half-life of a
radioactive isotope is the length of time required for one-half of a given number of
“parent” atoms to decay into stable “daughter” atoms. The relationship among parents,
daughters and half-life is illustrated below in Figure 1.
Figure 1
Radiometric dates reflect the time that has elapsed since a mineral formed and its
chemical composition was set. Because the dating procedure requires measuring the
existing amounts of parent and daughter isotopes, it is critically important to analyze
only those mineral grains that have remained closed systems since their time of origin.
A key requirement in radiometric dating is that there has been no loss or gain of parent
or daughter atoms through partial melting, metamorphism, weathering, or any other
agent.
Another requirement in radiometric dating is that no daughter atoms were originally
present in the grain to be analyzed. If some daughter atoms were originally present,
then they must be corrected for. And this goes for parent atoms as well. It is assumed
that no parent atoms were added or removed (by groundwater, faulting etc) or
corrections should be made if there is evidence that the system was partially open.
Table 1 lists some commonly used radioactive parents /daughters, their half-lives, λs,
and effective dating ranges, where λ is the decay constant (0.693/ half-life)
For 238U/206Pb dating, a general relationship can be written as follows:
Where Dp = present amount of daughter
Di = initial amount of daughter
Pp = present amount of parent
T = time in years since crystallization of the grain
This can be done for most isotopic systems. Finally, because 14C has a very short halflife, the 14C method is useful in dating organic material only as old as about 70,000
years. Laboratory work using very precise, Geiger counter-like instruments established
a relationship between the “specific activity” of an organic substance and its age.
Specific activity is a measure of the amount of remaining 14C, expressed in
counts/min/gm of material. See graph below. This graph plots Specific Activity vs Time
in thousands of years.
Figure 2: Decay curve for 14C
Exercise: Using Radiometric Dating to Help Determine the Geologic History of an
Area.
Isotopic analyses have been carried out on minerals separated from the three crystalline rocks
A, B, and C. These data are listed below the cross-section in Table 1. To calculate the ages of
the units, you will need to understand the principles of radiometric dating that you learned in
lecture. In this problem, we will be using the potassium-argon system; potassium-40 has a halflife of 1.25 billion years. Please show all of your mathematical work, and put a box around
As the rock ages, the amount of the parent isotope will decrease and the amount of the
daughter isotope will increase geometrically (not linearly). Graphs of radioactive decay clearly
show this geometrical or exponential decay. To determine the age of an unknown rock, you
need to measure the number of parent and daughter atoms in a sample (this data is given to
you in the table). If you know the half-life as well as the number of atoms of both isotopes, you
can calculate the age in years – an absolute age
TABLE 1: Results of Isotopic Analyses:
Rock Unit
Number of Parent Atoms
Number of Daughter Atoms
A
7497
1071
B
11480
3827
C
839
2517
Find the percents parent atoms for each rock unit above. You can use the per
cent parent left (divide number of parent atoms by the total number of atoms) or
you can estimate the number of half-lives by using the following graph.
Calculations:
Plot of Parent Amount versus Time (in half-lives)
110
100
90
Remaining Parent Isotope (%)
80
70
60
Series1
50
40
30
20
10
0
0
1
2
3
4
Half-Lives
5
6
7
8
Study Area Cross-Section
Develop a relative scale for the events shown in the diagram above. Use your
calculated radiometric dates to determine when events A, B and C occurred. Using the
geologic time scale, during which geologic periods did these events occur?
Lab 6A: Relative and absolute dating of geologic events
Part A: Relative Time Scales
Introduction
The study of Earth history involves determining the sequence of geologic events over
immense spans of time. In most cases the correct order of events can be determined
without knowing their actual ages: that is, we simply establish that event B occurred
before event C, but after event A. Such dating, in which the occurrence of events is
determined relative to one another, is known as relative dating. Of course it is always
useful to know the actual ages of rocks and events, if possible. Actual ages are
determined by means of radiometric dating techniques. Although several techniques
exist, all rely on the fact that radioactive “parent” isotopes decay into stable “daughter”
isotopes at a constant rate. With knowledge of the decay rate, ratios of parent and
daughter isotopes then can be used to derive an absolute date, in years, for
the age of a given mineral sample. The purpose of this lab is to introduce the principles
and concepts associated with both relative and absolute dating.
Relative dating
The relative order of geologic events can be established in most cases by applying four
or fewer basic principles:
1) The Principle of Original Horizontality states that sedimentary rocks are deposited
as horizontal or nearly horizontal layers. Any marked deviation from horizontality
indicates that some movement or deformation of the Earth’s crust occurred after
deposition of the inclined layer.
2) The Principle of Superposition states that in an ordinary vertical sequence of
sedimentary rocks, the layer at the bottom of the sequence is oldest, and successively
higher layers are successively younger.
3) The Principle of Cross-cutting relationships states that geologic features such as
faults and igneous intrusions, which cut through rocks, must be younger than the rocks
through which they cut.
4) The Principle of Inclusion states that if rocks or rock fragments are included within
another rock layer, the rock fragments must be older than the layer in which they are
included.
Complete Exercises I – V on the following pages.
Unconformities: Unconformities are especially useful in reconstructing Earth history.
An unconformity is a surface that corresponds with a gap in sedimentation,
either non-deposition or erosion. Rocks above an unconformity are younger than those
below it.
Three main types of unconformities are recognized (Figure 1):
1) angular unconformity, in which beds above and below the surface are not parallel
2) nonconformity, in which sedimentary layers overly crystalline rocks (either igneous
or metamorphic)
3) disconformity, in which beds above and below the surface are parallel, but the
surface itself is irregular, exhibiting evidence of erosional relief. In geologic block
diagrams and cross-sections, unconformities are usually drawn as a wavy line.
Figure 1
There is also a fourth type called a paraconformity where there is no obvious break in
the sedimentary record, but other evidence points to missing time.
I. Unconformities Exercises:
Figure 2: Possible unconformities
A
B
C
For each of the above, determine whether there is an unconformity. Give your reasoning
for each example above. Determine any missing time for the unconformities identified.
A:
B:
C:
II. Principle of Inclusions
Figure 3: Relative age from inclusion
D
E
For each of the above, determine the relative ages
D:
E:
F:
F
III. Principle of cross-cutting relations
Figure 4: Relative age determination using cross-cutting relations
G
H
I
For each of the above, determine the relative ages
G:
H:
I:
IV. Relative Dating Exercises – Telling the Story
For each of the following four block diagrams (A–D), determine the correct order in
which the various rock units and other features occurred. Write a summary for each
section detailing the occurrence of any unconformities and the timing of any intrusions
geologic structures etc.
A.
B.
C.
D.
Summary Paragraphs: Include in your summaries how the 4 principles outlined in
Diagram A:
Diagram B:
Diagram C:
Diagram D:
Part B: ABSOLUTE TIME SCALES
Background: Determination of the actual age, in years, of minerals is accomplished by
occurring isotopes are radioactive and their decay rates are constant. The half-life of a
radioactive isotope is the length of time required for one-half of a given number of
“parent” atoms to decay into stable “daughter” atoms. The relationship among parents,
daughters and half-life is illustrated below in Figure 1.
Figure 1
Radiometric dates reflect the time that has elapsed since a mineral formed and its
chemical composition was set. Because the dating procedure requires measuring the
existing amounts of parent and daughter isotopes, it is critically important to analyze
only those mineral grains that have remained closed systems since their time of origin.
A key requirement in radiometric dating is that there has been no loss or gain of parent
or daughter atoms through partial melting, metamorphism, weathering, or any other
agent.
Another requirement in radiometric dating is that no daughter atoms were originally
present in the grain to be analyzed. If some daughter atoms were originally present,
then they must be corrected for. And this goes for parent atoms as well. It is assumed
that no parent atoms were added or removed (by groundwater, faulting etc) or
corrections should be made if there is evidence that the system was partially open.
Table 1 lists some commonly used radioactive parents /daughters, their half-lives, λs,
and effective dating ranges, where λ is the decay constant (0.693/ half-life)
For 238U/206Pb dating, a general relationship can be written as follows:
Where Dp = present amount of daughter
Di = initial amount of daughter
Pp = present amount of parent
T = time in years since crystallization of the grain
This can be done for most isotopic systems. Finally, because 14C has a very short halflife, the 14C method is useful in dating organic material only as old as about 70,000
years. Laboratory work using very precise, Geiger counter-like instruments established
a relationship between the “specific activity” of an organic substance and its age.
Specific activity is a measure of the amount of remaining 14C, expressed in
counts/min/gm of material. See graph below. This graph plots Specific Activity vs Time
in thousands of years.
Figure 2: Decay curve for 14C
Exercise: Using Radiometric Dating to Help Determine the Geologic History of an
Area.
Isotopic analyses have been carried out on minerals separated from the three crystalline rocks
A, B, and C. These data are listed below the cross-section in Table 1. To calculate the ages of
the units, you will need to understand the principles of radiometric dating that you learned in
lecture. In this problem, we will be using the potassium-argon system; potassium-40 has a halflife of 1.25 billion years. Please show all of your mathematical work, and put a box around
As the rock ages, the amount of the parent isotope will decrease and the amount of the
daughter isotope will increase geometrically (not linearly). Graphs of radioactive decay clearly
show this geometrical or exponential decay. To determine the age of an unknown rock, you
need to measure the number of parent and daughter atoms in a sample (this data is given to
you in the table). If you know the half-life as well as the number of atoms of both isotopes, you
can calculate the age in years – an absolute age
TABLE 1: Results of Isotopic Analyses:
Rock Unit
Number of Parent Atoms
Number of Daughter Atoms
A
7497
1071
B
11480
3827
C
839
2517
Find the percents parent atoms for each rock unit above. You can use the per
cent parent left (divide number of parent atoms by the total number of atoms) or
you can estimate the number of half-lives by using the following graph.
Calculations:
Plot of Parent Amount versus Time (in half-lives)
110
100
90
Remaining Parent Isotope (%)
80
70
60
Series1
50
40
30
20
10
0
0
1
2
3
4
Half-Lives
5
6
7
8
Study Area Cross-Section
Develop a relative scale for the events shown in the diagram above. Use your
calculated radiometric dates to determine when events A, B and C occurred. Using the
geologic time scale, during which geologic periods did these events occur?
Lab 6A: Relative and absolute dating of geologic events
Part A: Relative Time Scales
Introduction
The study of Earth history involves determining the sequence of geologic events over
immense spans of time. In most cases the correct order of events can be determined
without knowing their actual ages: that is, we simply establish that event B occurred
before event C, but after event A. Such dating, in which the occurrence of events is
determined relative to one another, is known as relative dating. Of course it is always
useful to know the actual ages of rocks and events, if possible. Actual ages are
determined by means of radiometric dating techniques. Although several techniques
exist, all rely on the fact that radioactive “parent” isotopes decay into stable “daughter”
isotopes at a constant rate. With knowledge of the decay rate, ratios of parent and
daughter isotopes then can be used to derive an absolute date, in years, for
the age of a given mineral sample. The purpose of this lab is to introduce the principles
and concepts associated with both relative and absolute dating.
Relative dating
The relative order of geologic events can be established in most cases by applying four
or fewer basic principles:
1) The Principle of Original Horizontality states that sedimentary rocks are deposited
as horizontal or nearly horizontal layers. Any marked deviation from horizontality
indicates that some movement or deformation of the Earth’s crust occurred after
deposition of the inclined layer.
2) The Principle of Superposition states that in an ordinary vertical sequence of
sedimentary rocks, the layer at the bottom of the sequence is oldest, and successively
higher layers are successively younger.
3) The Principle of Cross-cutting relationships states that geologic features such as
faults and igneous intrusions, which cut through rocks, must be younger than the rocks
through which they cut.
4) The Principle of Inclusion states that if rocks or rock fragments are included within
another rock layer, the rock fragments must be older than the layer in which they are
included.
Complete Exercises I – V on the following pages.
Unconformities: Unconformities are especially useful in reconstructing Earth history.
An unconformity is a surface that corresponds with a gap in sedimentation,
either non-deposition or erosion. Rocks above an unconformity are younger than those
below it.
Three main types of unconformities are recognized (Figure 1):
1) angular unconformity, in which beds above and below the surface are not parallel
2) nonconformity, in which sedimentary layers overly crystalline rocks (either igneous
or metamorphic)
3) disconformity, in which beds above and below the surface are parallel, but the
surface itself is irregular, exhibiting evidence of erosional relief. In geologic block
diagrams and cross-sections, unconformities are usually drawn as a wavy line.
Figure 1
There is also a fourth type called a paraconformity where there is no obvious break in
the sedimentary record, but other evidence points to missing time.
I. Unconformities Exercises:
Figure 2: Possible unconformities
A
B
C
For each of the above, determine whether there is an unconformity. Give your reasoning
for each example above. Determine any missing time for the unconformities identified.
A:
B:
C:
II. Principle of Inclusions
Figure 3: Relative age from inclusion
D
E
For each of the above, determine the relative ages
D:
E:
F:
F
III. Principle of cross-cutting relations
Figure 4: Relative age determination using cross-cutting relations
G
H
I
For each of the above, determine the relative ages
G:
H:
I:
IV. Relative Dating Exercises – Telling the Story
For each of the following four block diagrams (A–D), determine the correct order in
which the various rock units and other features occurred. Write a summary for each
section detailing the occurrence of any unconformities and the timing of any intrusions
geologic structures etc.
A.
B.
C.
D.
Summary Paragraphs: Include in your summaries how the 4 principles outlined in
Diagram A:
Diagram B:
Diagram C:
Diagram D:
Part B: ABSOLUTE TIME SCALES
Background: Determination of the actual age, in years, of minerals is accomplished by
occurring isotopes are radioactive and their decay rates are constant. The half-life of a
radioactive isotope is the length of time required for one-half of a given number of
“parent” atoms to decay into stable “daughter” atoms. The relationship among parents,
daughters and half-life is illustrated below in Figure 1.
Figure 1
Radiometric dates reflect the time that has elapsed since a mineral formed and its
chemical composition was set. Because the dating procedure requires measuring the
existing amounts of parent and daughter isotopes, it is critically important to analyze
only those mineral grains that have remained closed systems since their time of origin.
A key requirement in radiometric dating is that there has been no loss or gain of parent
or daughter atoms through partial melting, metamorphism, weathering, or any other
agent.
Another requirement in radiometric dating is that no daughter atoms were originally
present in the grain to be analyzed. If some daughter atoms were originally present,
then they must be corrected for. And this goes for parent atoms as well. It is assumed
that no parent atoms were added or removed (by groundwater, faulting etc) or
corrections should be made if there is evidence that the system was partially open.
Table 1 lists some commonly used radioactive parents /daughters, their half-lives, λs,
and effective dating ranges, where λ is the decay constant (0.693/ half-life)
For 238U/206Pb dating, a general relationship can be written as follows:
Where Dp = present amount of daughter
Di = initial amount of daughter
Pp = present amount of parent
T = time in years since crystallization of the grain
This can be done for most isotopic systems. Finally, because 14C has a very short halflife, the 14C method is useful in dating organic material only as old as about 70,000
years. Laboratory work using very precise, Geiger counter-like instruments established
a relationship between the “specific activity” of an organic substance and its age.
Specific activity is a measure of the amount of remaining 14C, expressed in
counts/min/gm of material. See graph below. This graph plots Specific Activity vs Time
in thousands of years.
Figure 2: Decay curve for 14C
Exercise: Using Radiometric Dating to Help Determine the Geologic History of an
Area.
Isotopic analyses have been carried out on minerals separated from the three crystalline rocks
A, B, and C. These data are listed below the cross-section in Table 1. To calculate the ages of
the units, you will need to understand the principles of radiometric dating that you learned in
lecture. In this problem, we will be using the potassium-argon system; potassium-40 has a halflife of 1.25 billion years. Please show all of your mathematical work, and put a box around
As the rock ages, the amount of the parent isotope will decrease and the amount of the
daughter isotope will increase geometrically (not linearly). Graphs of radioactive decay clearly
show this geometrical or exponential decay. To determine the age of an unknown rock, you
need to measure the number of parent and daughter atoms in a sample (this data is given to
you in the table). If you know the half-life as well as the number of atoms of both isotopes, you
can calculate the age in years – an absolute age
TABLE 1: Results of Isotopic Analyses:
Rock Unit
Number of Parent Atoms
Number of Daughter Atoms
A
7497
1071
B
11480
3827
C
839
2517
Find the percents parent atoms for each rock unit above. You can use the per
cent parent left (divide number of parent atoms by the total number of atoms) or
you can estimate the number of half-lives by using the following graph.
Calculations:
Plot of Parent Amount versus Time (in half-lives)
110
100
90
Remaining Parent Isotope (%)
80
70
60
Series1
50
40
30
20
10
0
0
1
2
3
4
Half-Lives
5
6
7
8
Study Area Cross-Section
Develop a relative scale for the events shown in the diagram above. Use your
calculated radiometric dates to determine when events A, B and C occurred. Using the
geologic time scale, during which geologic periods did these events occur?
Lab 6A: Relative and absolute dating of geologic events
Part A: Relative Time Scales
Introduction
The study of Earth history involves determining the sequence of geologic events over
immense spans of time. In most cases the correct order of events can be determined
without knowing their actual ages: that is, we simply establish that event B occurred
before event C, but after event A. Such dating, in which the occurrence of events is
determined relative to one another, is known as relative dating. Of course it is always
useful to know the actual ages of rocks and events, if possible. Actual ages are
determined by means of radiometric dating techniques. Although several techniques
exist, all rely on the fact that radioactive “parent” isotopes decay into stable “daughter”
isotopes at a constant rate. With knowledge of the decay rate, ratios of parent and
daughter isotopes then can be used to derive an absolute date, in years, for
the age of a given mineral sample. The purpose of this lab is to introduce the principles
and concepts associated with both relative and absolute dating.
Relative dating
The relative order of geologic events can be established in most cases by applying four
or fewer basic principles:
1) The Principle of Original Horizontality states that sedimentary rocks are deposited
as horizontal or nearly horizontal layers. Any marked deviation from horizontality
indicates that some movement or deformation of the Earth’s crust occurred after
deposition of the inclined layer.
2) The Principle of Superposition states that in an ordinary vertical sequence of
sedimentary rocks, the layer at the bottom of the sequence is oldest, and successively
higher layers are successively younger.
3) The Principle of Cross-cutting relationships states that geologic features such as
faults and igneous intrusions, which cut through rocks, must be younger than the rocks
through which they cut.
4) The Principle of Inclusion states that if rocks or rock fragments are included within
another rock layer, the rock fragments must be older than the layer in which they are
included.
Complete Exercises I – V on the following pages.
Unconformities: Unconformities are especially useful in reconstructing Earth history.
An unconformity is a surface that corresponds with a gap in sedimentation,
either non-deposition or erosion. Rocks above an unconformity are younger than those
below it.
Three main types of unconformities are recognized (Figure 1):
1) angular unconformity, in which beds above and below the surface are not parallel
2) nonconformity, in which sedimentary layers overly crystalline rocks (either igneous
or metamorphic)
3) disconformity, in which beds above and below the surface are parallel, but the
surface itself is irregular, exhibiting evidence of erosional relief. In geologic block
diagrams and cross-sections, unconformities are usually drawn as a wavy line.
Figure 1
There is also a fourth type called a paraconformity where there is no obvious break in
the sedimentary record, but other evidence points to missing time.
I. Unconformities Exercises:
Figure 2: Possible unconformities
A
B
C
For each of the above, determine whether there is an unconformity. Give your reasoning
for each example above. Determine any missing time for the unconformities identified.
A:
B:
C:
II. Principle of Inclusions
Figure 3: Relative age from inclusion
D
E
For each of the above, determine the relative ages
D:
E:
F:
F
III. Principle of cross-cutting relations
Figure 4: Relative age determination using cross-cutting relations
G
H
I
For each of the above, determine the relative ages
G:
H:
I:
IV. Relative Dating Exercises – Telling the Story
For each of the following four block diagrams (A–D), determine the correct order in
which the various rock units and other features occurred. Write a summary for each
section detailing the occurrence of any unconformities and the timing of any intrusions
geologic structures etc.
A.
B.
C.
D.
Summary Paragraphs: Include in your summaries how the 4 principles outlined in
Diagram A:
Diagram B:
Diagram C:
Diagram D:
Part B: ABSOLUTE TIME SCALES
Background: Determination of the actual age, in years, of minerals is accomplished by
occurring isotopes are radioactive and their decay rates are constant. The half-life of a
radioactive isotope is the length of time required for one-half of a given number of
“parent” atoms to decay into stable “daughter” atoms. The relationship among parents,
daughters and half-life is illustrated below in Figure 1.
Figure 1
Radiometric dates reflect the time that has elapsed since a mineral formed and its
chemical composition was set. Because the dating procedure requires measuring the
existing amounts of parent and daughter isotopes, it is critically important to analyze
only those mineral grains that have remained closed systems since their time of origin.
A key requirement in radiometric dating is that there has been no loss or gain of parent
or daughter atoms through partial melting, metamorphism, weathering, or any other
agent.
Another requirement in radiometric dating is that no daughter atoms were originally
present in the grain to be analyzed. If some daughter atoms were originally present,
then they must be corrected for. And this goes for parent atoms as well. It is assumed
that no parent atoms were added or removed (by groundwater, faulting etc) or
corrections should be made if there is evidence that the system was partially open.
Table 1 lists some commonly used radioactive parents /daughters, their half-lives, λs,
and effective dating ranges, where λ is the decay constant (0.693/ half-life)
For 238U/206Pb dating, a general relationship can be written as follows:
Where Dp = present amount of daughter
Di = initial amount of daughter
Pp = present amount of parent
T = time in years since crystallization of the grain
This can be done for most isotopic systems. Finally, because 14C has a very short halflife, the 14C method is useful in dating organic material only as old as about 70,000
years. Laboratory work using very precise, Geiger counter-like instruments established
a relationship between the “specific activity” of an organic substance and its age.
Specific activity is a measure of the amount of remaining 14C, expressed in
counts/min/gm of material. See graph below. This graph plots Specific Activity vs Time
in thousands of years.
Figure 2: Decay curve for 14C
Exercise: Using Radiometric Dating to Help Determine the Geologic History of an
Area.
Isotopic analyses have been carried out on minerals separated from the three crystalline rocks
A, B, and C. These data are listed below the cross-section in Table 1. To calculate the ages of
the units, you will need to understand the principles of radiometric dating that you learned in
lecture. In this problem, we will be using the potassium-argon system; potassium-40 has a halflife of 1.25 billion years. Please show all of your mathematical work, and put a box around
As the rock ages, the amount of the parent isotope will decrease and the amount of the
daughter isotope will increase geometrically (not linearly). Graphs of radioactive decay clearly
show this geometrical or exponential decay. To determine the age of an unknown rock, you
need to measure the number of parent and daughter atoms in a sample (this data is given to
you in the table). If you know the half-life as well as the number of atoms of both isotopes, you
can calculate the age in years – an absolute age
TABLE 1: Results of Isotopic Analyses:
Rock Unit
Number of Parent Atoms
Number of Daughter Atoms
A
7497
1071
B
11480
3827
C
839
2517
Find the percents parent atoms for each rock unit above. You can use the per
cent parent left (divide number of parent atoms by the total number of atoms) or
you can estimate the number of half-lives by using the following graph.
Calculations:
Plot of Parent Amount versus Time (in half-lives)
110
100
90
Remaining Parent Isotope (%)
80
70
60
Series1
50
40
30
20
10
0
0
1
2
3
4
Half-Lives
5
6
7
8
Study Area Cross-Section
Develop a relative scale for the events shown in the diagram above. Use your
calculated radiometric dates to determine when events A, B and C occurred. Using the
geologic time scale, during which geologic periods did these events occur?

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